Tag: cosθ

Consider a right-angled triangle ABC below.

The angle θ can be expressed in terms of cosine ratio or sine ratio. The hypotenuse of the triangle has dimension r.

Adjacent side to angle θ is the line AB and the opposite side to the angle θ  is line BC.

expressing angle θ  in terms of cosine ratio and sin ratio:

by use of Pythagoras theorem:

(AB)² + (BC)² = r²

(rcosθ)² + (rcosθ)² = r² and hence

r² cos² θ + r² sin² θ  = r²

then dividing everywhere by r² , then we get

cos² θ + sin² θ  =1 which is a trigonometric identity which holds true for all values of  θ.

Example

If tan θ = a, show that:

solution

we factor out cosθ to get:

but sin² θ + cos² θ  =1

hence:

but tanθ = a, so 1/tanθ = 1/a

Related Topics

• Using tangents to solve triangles
• Table of tangents
• Equations of a circle
• Trigonometry
• Angle Tangents

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